Fourier optics

This expression is the main tool used in describing diffraction effects associated with Fourier optics. Holographic techniques and effects can, likewise, be approached similarly by describing first the plane wave case which can then be generalized to address more complex distribution problems by using the same superposition principle. 

Smith, W.J., 2000, Modern Optical Engineering, McGraw Hill, 3rd Ed Kingslake, R., Academic Press, 1983, Optical System Design Goodman, J.W., 1996, Introduction of Fourier Optics 2nd Ed, McGraw Hill Bom, M., Wolf, E., 1999, Principle of Optics 7th Ed, Cambridge University Press... 

Fried, D.L., 1966, Optical Resolution through a randomly inhomogeneous medium for very long and very short exposures, JOSA. A 56, 1376 Goodman, J., 1996, Introduction to Fourier optics (McGraw-Hill, New York), pp. 63-75. 

Goodman, J. W. "Introduction to Fourier Optics" McGraw Hill New York, 1968, Chap. 1-3. 

Gold, R. (1964). An Iterative Unfolding Method for Response Matrices. AEC Research and Development Report ANL-6984, Argonne National Laboratory, Argonne, Illinois. Goodman, J. W. (1968). Introduction to Fourier Optics. McGraw-Hill, New York. 

J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, New York, 1996. 

For a somewhat more accurate estimate of the apparent source size in particular emission and observation conditions, numerical methods of Fourier optics can be used. In this framework, the effective source size can be obtained either by backpropagation of the wavefront (at a specific wavenumber) to the source position, or by simulating the radiation focusing at optical magnification equal to 1. To illustrate this, we have considered two cases an IR beamline at the NSLS (0.8 GeV storage ring) normalized at 1000 mA (electron source size = 550 p,m horizontal, 70 (im vertical) and an IR beamline at SOFFIT, (2.75 GeV - electron source... 

Now we must examine the physics of image formation by a lens more closely, and to do this we must introduce the ideas of Fourier optics. It would be inappropriate here to develop fully these ideas, as is done in most modern textbooks on optics, but it is important to understand clearly the fundamental concepts of Fourier optics because we shall need them when we deal specifically with electron diffraction. However, before continuing, it is necessary to digress briefly to introduce the mathematics used to describe plane and spherical waves. 

Image formation by a thin lens in terms of Fourier optics ... 

Figure 1.6. (a) Diagram showing the general geometry and coordinates used for discussing image formation by a lens in terms of Fourier optics, (b) Path difference between two parallel rays from points O and Q in the xy plane. 

E. G. Steward. Fourier Optics An Introduction. 2nd edn. Ellis Horwood ... 

Qiu, H.-H. and Hsu, C.T., A Fourier optics method for the simulation of measurement volume effect by the slit constraint. Proceedings of the Eigth International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, Vol. 1, Paper 12.6 (1996)... 

A laser beam is passed through the measurement cell and brought to a waist of focus at the plane of the multielement detector. This is the reverse Fourier optical setup. Conventional Fourier optics arrangements are also used. 

This is covered in many optics texts, including S. G. Lipson, H. Lipson, and D. S. Taimen-baum, Optical Physics, 3rd ed., Cambridge University Press, 1995, Ch, 12 J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill, 1968, Ch. 6. 

E.G. Steward, Fourier Optics, An Introduction, Wiley, New York, 1983. 

The following treatise presupposes a general knowledge of the Xnray diffraction theory, especially of small-ai e X-ray diffraction and famOarity with the laws of Fourier-optics. Pertinent information may be obtained from the book of Hosemann and Bagchi An introductory presentation of this theory is also given in the summer school lectures on the Biophysics of Membranes held in Vancourer in 1974 by Kreutz and Pape l... 

X-ray scattering can be desmbed by the laws of Fourier-optics which are summarized in the following diagram ... 

Several references were used extensively in the mathematical treatments shown below. These ate Introduction to Solid State Physics by C. Kittel (6), Solid State Physics by Ashcroft and Mermin (7), Diffraction Pfysics by Cowley (8) and Fourier Optics an Introduction by Steward (9). While ttrese books do not consider polymers specifically, they have excellent general treatments cf scattering fiom crystals. Cowley s... 

Cowley Diffraction Physics, 2nd Ed. Norfti Holland Amsterdam, 1981. Steward Fourier Optics an Introduction Ellis Horwood Limited Chichester, 1983. 

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